In the oil and gas field, it is important to be able to produce accurate models of subterranean, or subsurface, regions, such as of subsurface structures and features, fluids, properties, and related parameters thereof. Illustrative, non-exclusive examples of such fluids include liquid and gaseous hydrocarbons and water. Illustrative, non-exclusive examples of such parameters include temperature, pressure, permeability, porosity, shear and/or strain forces, compaction, fluid properties, subsurface formation properties, in situ reservoir conditions, Poisson's ratio, modulus of elasticity, shear modulus, strength, compressibility, combinations thereof, and the like. Illustrative, non-exclusive examples of such structures include reservoirs, wells and wellbores, well orifices, near wellbore surfaces, subsurface strata, producer fields, stimulated formation structures such as fractures and acid wormholes, and the like.
Some of the most precise information and tools are available from full-field models, which also may be referred to as full-physics models. These models are complex, fine-scale computer simulations of the subterranean region to be modeled, and may be based on the fundamental physics of the parameter(s) to be modeled in the subterranean region. The full-physics models are computationally-intensive, demanding implicit models that take significant amounts of time and resources to prepare, validate, and implement. The time required refers to the number of hours that individuals must spend to prepare, validate, and implement the model, with this time typically being performed by one or more of a relatively limited number of individuals with sufficient training and technical expertise to create these models. For example, these individuals may be highly trained individuals having expert knowledge of reservoir fluid flow mechanics, geomechanics, and mathematical modeling of dynamic bodies. In addition, the computational resources required to prepare, validate, and implement these models typically require specialized software and powerful computers.
These full-physics models may be used for such illustrative purposes as to simulate and/or predict future values, performance, responses to changes in variables, etc. of the corresponding subsurface region, or portions thereof. Specific illustrative, non-exclusive examples include modeling hydrocarbon flow from producer wells, predicting water flow, modeling injectivity of a formation, and modeling well operability limits, which may refer to the ability of a well to withstand changes in subsurface geomechanical stresses.
While very effective at accurately simulating and predicting characteristics and/or responses of the modeled subterranean region, full-physics models suffer the above-discussed limitations due to their computational and resource demands, including the time demands of highly experienced operators. Moreover, full-physics models suffer from limitations in their ability to process information in real time, as individual iterations may take many hours or days to calculate a single response. This may make it impractical to rely on these full-physics models for day-to-day decision making, such as by an operator in the field. Furthermore, new models generally must be developed for each particular well, near-wellbore, or other subsurface region of interest because full-physics models are directed to a specific application or region. However, the time and resource demands discussed above often render it impractical to conduct different simulations and/or to utilize the complicated physics-based models during each life cycle phase of a well or other subsurface region.
Other mathematical solutions exist, but they are based on stringent assumptions that are assumed to govern the interrelationship of various parameters. However, these assumptions often do not correspond to real-world subterranean conditions. For example, actual well and near-well operating conditions often deviate substantially from these assumptions. These assumptions often will include assuming that physical subterranean behavior is linear, or nearly linear, and that properties are constant and homogenous. As with the above-described fine-scale models, complicated numerical models may be developed to predict non-ideal behavior of subterranean surfaces. However, these models also are computationally complex and require operators with extensive training and experience. Moreover, these models are unique to particular parameters, such as geometry, properties, and boundary conditions.
More recently, surrogate representations, or models, of such fine-scale computer models have been developed. Surrogate modeling refers to the creation of representations of fine-scale computer models. Surrogate models are explicit mathematical functions that emulate, or mimic, the responses of implicit full-physics (fine-scale) models with high accuracy, but which are able to generate responses in a fraction of the time required to generate a response from the full-physics model from which the surrogate model was generated.
Surrogate models are useful tools, especially for field personnel and other users who may lack the time, expertise, and/or computational resources to utilize fine-scale computer models. As such, surrogate models have proven to be extremely useful for real-time, in-field analysis and decision-making For example, surrogate models may be distributed to front end users involved with well design and evaluation, enabling these users to perform high-end engineering analysis with minimal effort. In other words, surrogate models may be used to deliver high-end modeling capability to front-end (i.e., in the field) users. Illustrative, non-exclusive examples of conventional surrogate models may be found in U.S. Pat. No. 4,759,636, U.S. Patent Application Publication Nos. 2006/0160137 and 2007/0094187, and International Publication Nos. WO2007/018860, WO2007/018862, and WO2007/018858, the complete disclosures of which are hereby incorporated by reference herein.
A challenge of surrogate modeling is that surrogate models conventionally may be limited in their usefulness because they are limited to a single response at a single reference time. Specifically, such surrogates represent the current knowledge and computational capability at the time they were created and their responses are particular to the point in time for which they are generated. This time-specific nature of conventional surrogate models may result in a loss of accuracy and information compared to the full-physics model from which the surrogate model was generated, such as if an attempt is made to generalize the model for use in other applications and/or at other times. These limitations may be particularly apparent when the surrogates are designed for use to model subterranean regions that exhibit complex spatial and temporal behavior. In addition, computational capabilities and knowledge of the physics involved in a particular surrogate may quickly become outdated as available modeling capabilities and knowledge evolve. Re-running previous computer models and creating new surrogates, replacing previous surrogate models outright, or having contradictory surrogates can pose challenges.